We present a new algorithm for exactly solving decision-making problems represented as an influence diagram. We do not require the usual assumptions of no forgetting and regularity, which allows us to solve problems with limited information. The algorithm, which implements a sophisticated variable elimination procedure, is empirically shown to outperform a state-of-the-art algorithm in randomly generated problems of up to 150 variables and $10^{64}$ strategies.

Multi-class Gaussian Process Classifiers (MGPCs) are often affected by over-fitting problems when labeling errors occur far from the decision boundaries. To prevent this, we investigate a robust MGPC (RMGPC) which considers labeling errors independently of their distance to the decision boundaries. Expectation propagation is used for approximate inference. Experiments with several datasets in which noise is injected in the class labels illustrate the benefits of RMGPC. This method performs better than other Gaussian process alternatives based on considering latent Gaussian noise or heavy-tailed processes. When no noise is injected in the labels, RMGPC still performs equal or better than the other methods. Finally, we show how RMGPC can be used for successfully identifying data instances which are difficult to classify accurately in practice.

An important task in exploring and analyzing real-world data sets is to detect unusual and interesting phenomena. In this paper, we study the group anomaly detection problem. Unlike traditional anomaly detection research that focuses on data points, our goal is to discover anomalous aggregated behaviors of groups of points. For this purpose, we propose the Flexible Genre Model (FGM). FGM is designed to characterize data groups at both the point level and the group level so as to detect various types of group anomalies. We evaluate the effectiveness of FGM on both synthetic and real data sets including images and turbulence data, and show that it is superior to existing approaches in detecting group anomalies.

The difficulty in inverse reinforcement learning (IRL) arises in choosing the best reward function since there are typically an infinite number of reward functions that yield the given behaviour data as optimal. Using a Bayesian framework, we address this challenge by using the maximum a posteriori (MAP) estimation for the reward function, and show that most of the previous IRL algorithms can be modeled into our framework. We also present a gradient method for the MAP estimation based on the (sub)differentiability of the posterior distribution. We show the effectiveness of our approach by comparing the performance of the proposed method to those of the previous algorithms.

How do people determine which elements of a set are most representative of that set? We extend an existing Bayesian measure of representativeness, which indicates therepresentativeness of a sample from a distribution, to define a measure of the representativeness of an item to a set. We show that this measure is formally related to a machine learning method known as Bayesian Sets. Building on this connection, we derive an analytic expression for the representativeness of objects described by a sparse vector of binary features. We then apply this measure to a large database of images, using it to determine which images are the most representative membersof different sets. Comparing the resulting predictions to human judgments of representativeness provides a test of this measure with naturalistic stimuli, and illustrates how databases that are more commonly used in computer vision and machine learning can be used to evaluate psychological theories.

We consider the problem of Bayesian inference for continuous-time multi-stable stochastic systems which can change both their diffusion and drift parameters at discrete times. We propose exact inference and sampling methodologies for two specific cases where the discontinuous dynamics is given by a Poisson process and a two-state Markovian switch. We test the methodology on simulated data, and apply it to two real data sets in finance and systems biology. Our experimental results show that the approach leads to valid inferences and nontrivial insights.

We present an asymptotic analysis of Viterbi Training (VT) and contrast it with a more conventional Maximum Likelihood (ML) approach to parameter estimation in Hidden Markov Models. While ML estimator works by (locally) maximizing the likelihood of the observed data, VT seeks to maximize the probability of the most likely hidden state sequence. We develop an analytical framework based on a generating function formalism and illustrate it on an exactly solvable model of HMM with one unambiguous symbol. For this particular model the ML objective function is continuously degenerate. VT objective, in contrast, is shown to have only finite degeneracy. Furthermore, VT converges faster and results in sparser (simpler) models, thus realizing an automatic Occam's razor for HMM learning. For more general scenario VT can be worse compared to ML but still capable of correctly recovering most of the parameters.

For many real-world applications, we often need to select correlated variables---such as genetic variations and imaging features associated with Alzheimer's disease---in a high dimensional space. The correlation between variables presents a challenge to classical variable selection methods. To address this challenge, the elastic net has been developed and successfully applied to many applications. Despite its great success, the elastic net does not exploit the correlation information embedded in the data to select correlated variables. To overcome this limitation, we present a novel hybrid model, EigenNet, that uses the eigenstructures of data to guide variable selection. Specifically, it integrates a sparse conditional classification model with a generative model capturing variable correlations in a principled Bayesian framework. We develop an efficient active-set algorithm to estimate the model via evidence maximization. Experiments on synthetic data and imaging genetics data demonstrated the superior predictive performance of the EigenNet over the lasso, the elastic net, and the automatic relevance determination.

When used to learn high dimensional parametric probabilistic models, the clas- sical maximum likelihood (ML) learning often suffers from computational in- tractability, which motivates the active developments of non-ML learning meth- ods. Yet, because of their divergent motivations and forms, the objective func- tions of many non-ML learning methods are seemingly unrelated, and there lacks a unified framework to understand them. In this work, based on an information geometric view of parametric learning, we introduce a general non-ML learning principle termed as minimum KL contraction, where we seek optimal parameters that minimizes the contraction of the KL divergence between the two distributions after they are transformed with a KL contraction operator. We then show that the objective functions of several important or recently developed non-ML learn- ing methods, including contrastive divergence [12], noise-contrastive estimation [11], partial likelihood [7], non-local contrastive objectives [31], score match- ing [14], pseudo-likelihood [3], maximum conditional likelihood [17], maximum mutual information [2], maximum marginal likelihood [9], and conditional and marginal composite likelihood [24], can be unified under the minimum KL con- traction framework with different choices of the KL contraction operators.

The distance dependent Chinese restaurant process (ddCRP) was recently introduced toaccommodate random partitions of non-exchangeable data [1]. The dd-CRP clusters data in a biased way: each data point is more likely to be clustered with other data that are near it in an external sense. This paper examines the dd-CRP in a spatial setting with the goal of natural image segmentation. We explore the biases of the spatial ddCRP model and propose a novel hierarchical extension bettersuited for producing "humanlike" segmentations. We then study the sensitivity of the models to various distance and appearance hyperparameters, and provide the first rigorous comparison of nonparametric Bayesian models in the image segmentationdomain. On unsupervised image segmentation, we demonstrate that similar performance to existing nonparametric Bayesian models is possible with substantially simpler models and algorithms.